If x = 4, what is x^-3/2 ( x^100/ x^99)?

We'll start with the term
x^-3/2.

We'll apply the rule of the negative
power:

x^-n = 1/x^n

Now, we'll
substitute n by -3/2:

x^-3/2 =
1/x^3/2

Now, we'll compute the ratio
x^100/x^99.

Since the bases x are matching, we'll subtract
the exponents:

x^100/x^99 = x^(100-99) = x^1 =
x

We'll re-write the
expression:

x^-3/2(x^100/x^99) = x^(100-99)/x^3/2 =
x^1/x^3/2

x^-3/2(x^100/x^99) = x^(1 -
3/2)

x^-3/2(x^100/x^99) =
x^-1/2

x^-3/2(x^100/x^99) =
1/x^1/2

x^-3/2(x^100/x^99) = 1/sqrt
x

x^-3/2(x^100/x^99) = (sqrt
x)/x

We'll substitute x by
4:

(sqrt x)/x =
sqrt4/4

sqrt4/4 =
2/4

sqrt4/4 =
1/2